Problem: What do the following two equations represent? $x+y = 2$ $-4x+4y = -2$
Answer: Putting the first equation in $y = mx + b$ form gives: $x+y = 2$ $y = -x+2$ Putting the second equation in $y = mx + b$ form gives: $-4x+4y = -2$ $4y = 4x-2$ $y = 1x - \dfrac{1}{2}$ The slopes are negative inverses of each other, so the lines are perpendicular.